First-half goals from Sam Saunders and Clayton Donaldson put the Bees on the way to only their second win in the last seven league games.
Crawley were reduced to 10 men after just 50 seconds when defender Mark Connolly was sent off for a professional foul, and Brentford also had Adam Forshaw dismissed for diving before Nicky Adams pulled a goal back for the home side with a stunning 30-yard drive.
Rosler said: "All credit to Crawley, but I'm disappointed at how we used the extra man and the mistakes we made.
"The referee was poor, but we got the three points we needed. It was difficult to understand what we delivered on the field."
Donaldson missed a perfect opportunity to give his side an early lead from the penalty spot after he had been pulled down by Connolly, but wastefully blazed the spot-kick wide.
Rosler was annoyed that he took the penalty and said: "He's already missed this season and I should have overruled him from the outside.
"This is a case of us being happy with the three points and moving on. We must look beyond this result and do better."